The wheels on a skateboard have a diameter of 2.93 inches. If a skateboarder is traveling downhill at 23 miles per​ hour, determine the angular velocity of the wheels in radians per second.

The angular velocity of the wheels is 276.314 radians per second.

Explanation:

The wheels are rolling, which is a combination of rotation and translation, whose center of rotation is the point of contact between the wheel and the ground and the geometrical center of the skateboard experiments pure translation. Then, the angular velocity can be found by using the following kinematic expression:

(1)

Where:

- Angular velocity, in radians per second.

- Velocity of the wheel at its center, in inches per second.

- Radius of the wheel, in inches.

If we know that and , then the angular velocity of the wheels are:

The angular velocity of the wheels is 276.314 radians per second.

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6 cos 34, 6 sin 34 trig